Crystal structure and emission study of [(PPh3)2Cu(dmp)-O-(dmp)Cu(PPh3)2]2+ (dmp = 2,9-dimethyl-1,10-phenanthroline)

The synthesis and crystal structure of a luminescent dinuclear Cu(I) complex as the BF^– ₄ salt from toluene and methanol containing triphenylphosphine and -oxo-bis(2,9-dimethyl-1,10-phenanthroline) is described. The coordination geometry about the Cu(I) center is distorted tetrahedral. An unusual feature of the structure is a pseudo-inversion center located near the oxygen atom at approximately 0.51, 0.26, 0.25, such that all of the atoms except for the oxygen are related by a pseudo-inversion center to another atom in the same molecule, as well as by crystallographic inversion to the other molecule in the unit cell. The complex displays luminescence from an MLCT band in fluid solution and emission from both a metal-centered charge-transfer and intraligand (phenanthroline) state at 77K in a chloroform snow. Crystal data: triclinic, P , a = 15.163(2), b = 16.985(2), c = 18.731(2) Å, = 106.458(9), = 91.416(8), = 102.557(9)°, V = 4496(1) ų, and Z = 2.     

The Trace Conjecture – A Counterexample

In the paper Geometric K-Theory for Lie Groups and Foliations, Baum and Connes conjecture in a remark following Corollary 2 of their famous Isomorphism conjecture that for a finitely generated group with torsion, the trace map tr: K₀(C^*)R maps K₀(C^*) onto the additive subgroup of Q generated by all rational numbers of the form 1/n where n is the order of a finite subgroup of . We construct a counterexample to this conjecture.     

Self consistent modified extended Hückel (SC-MEH) calculations on heavy metal systems. I. Platinum(II) tetragonal planar complexes with and without relativistic effects

The Self Consistent Modified Extended Hückel molecular orbital method had been applied to several square planar complexes of platinum (II). Calculations including both the limited 5d, 6s, 6p and extended 5s, 5p, 5d, 6s, 6p starting bases for platinum were made. It is shown that in PtCl ₄ ^2– both the nuclear quadrupole moment and minimum total energy vs. bond distance are calculated to be in good agreement with experiment, only with the extended platinum AO basis.Specific inclusion of relativistic parameters via a pseudo-relativistic approximation are shown to have a significant effect on the energy molecular energy levels, however no meaningful rationalization can be made without the simultaneous inclusion of ligand field parameters as well.Supported in part by a grant made available through the Cancer Association of Greater New Orleans. Use of the facilities of the Computer Research Center of the University of New Orleans is gratefully acknowledged.     

Shell energy in the heaviest nuclei using the Green’s function oscillator expansion method

The Greens function oscillator expansion method and the generalized Strutinsky smoothing procedure are applied to shell corrections in the heaviest elements. A macroscopic-microscopic method with a finite deformed Woods-Saxon potential is used. The stability condition for the shell correction is discussed in detail and the parameters defining the smoothing procedure are carefully determined. It is demonstrated that the spurious contribution to the total binding energy due to the unphysical particle gas that appears in the standard method can be as large as 1.5 MeV for weakly bound neutron-rich superheavy nuclei, but the effect on energy differences (e.g., alpha-decay values) is fairly small.     

Eikonal approximation to 5D wave equations as geodesic motion in a curved 4D spacetime

We first derive the relation between the eikonal approximation to the Maxwell wave equations in an inhomogeneous anisotropic medium and geodesic motion in a three dimensional Riemannian manifold using a method which identifies the symplectic structure of the corresponding mechanics. We then apply an analogous method to the five dimensional generalization of Maxwell theory required by the gauge invariance of Stueckelbergs covariant classical and quantum dynamics to demonstrate, in the eikonal approximation, the existence of geodesic motion for the flow of mass in a four dimensional pseudo-Riemannian manifold. No motion of the medium is required. These results provide a foundation for the geometrical optics of the five dimensional radiation theory and establish a model in which there is mass flow along geodesics. Finally, we discuss the interesting case of relativistic quantum theory in an anisotropic medium as well. In this case the eikonal approximation to the relativistic quantum mechanical current coincides with the geodesic flow governed by the pseudo-Riemannian metric obtained from the eikonal approximation to solutions of the Stueckelberg-Schrödinger equation. This construction provides a model for an underlying quantum mechanical structure for classical dynamical motion along geodesics on a pseudo-Riemannian manifold. The locally symplectic structure which emerges is that of Stueckelbergs covariant mechanics on this manifold.This revised version was published online in April 2005. The publishing date was inserted.     

Synthesis of alkyl (α-phenylthioalkenyl) ketones containing a (Z)-trisubstituted olefinic fragment

Warren"s method, which has been proposed for the synthesis of -phenylthiodialkyl ketones, appeared to be inefficient for the preparation of their alkenyl alkyl analogs. The latter were prepared in good yields by alkenylation of alkyl phenylthiomethyl ketones with alkenyl bromides.     

Synthesis of 4-phenyl-3,4-dihydro-β-carboline

4-Phenyl-3,4-dihydro--carboline was prepared using the Bischler—Napieralski reaction on -phenyltryptamine.Translated from Khimiya Prirodnykh Soedinenii, No. 6, pp. 486–487, November–December, 2004.This revised version was published online in April 2005 with a corrected cover date.     

Stress State of an Elastic Space with a Toroidal‐Shaped Cavity

Solutions are obtained for the stress state problem for an elastic space with an internal toroidalshaped cavity that can be expanded in a trigonometric series in the angle in cylindrical coordinates. Displacements and stresses are specified on the boundary. An analytic solution of the problem is found using generalized analytic functions. Stresses and displacements of points in the elastic space are calculated.     

On Tori Triangulations Associated with Two-Dimensional Continued Fractions of Cubic Irrationalities

The notion of equivalence of multidimensional continued fractions is introduced. We consider some properties and state some conjectures related to the structure of the family of equivalence classes of two-dimensional periodic continued fractions. Our approach to the study of the family of equivalence classes of two-dimensional periodic continued fractions leads to revealing special subfamilies of continued fractions for which the triangulations of the torus (i.e., the combinatorics of their fundamental domains) are subjected to clear rules. Some of these subfamilies are studied in detail; the way to construct other similar subfamilies is indicated.     

Hopf-Lax type formula for non monotonic autonomous Hamilton Jacobi equations

We give an explicit formula for a solution of Hamilton-Jacobi equation u_t+H(u,Du)=0 in with initial condition u(x,0)=u₀(x), where p H(u,p) is convex, positively homogeneous of degree one and the Hamiltonian H need not satisfy the monotonicity condition in u.